When heavy ions meet cosmic rays: potential impact of QGP

PoS(ICRC2021)469

ICRC 2021THE ASTROPARTICLE PHYSICS CONFERENCE

Berlin | Germany

ONLINE ICRC 2021THE ASTROPARTICLE PHYSICS CONFERENCE

Berlin | Germany

37th International Cosmic Ray Conference

12–23 July 2021

When heavy ions meet cosmic rays: potential impact ofQGP formation on the muon puzzle

Tanguy Pierog,0,∗ Sebastian Baur,1 Hans Dembinski,2 Matias Perlin,0,3 Ralf Ulrich0and Klaus Werner4

0KIT, IAP, Karlsruhe, Germany1Université Libre de Bruxelles, IIHE, Brussels, Belgium2Experimentelle Physik 5, TU Dortmund, Germany3Instituto de Tecnologías en Detección y Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires,Argentina

3SUBATECH, University of Nantes – IN2P3/CNRS – IMT Atlantique, Nantes, FranceE-mail: [email protected]

The deficit of muons in the simulation of extensive air showers is a long-standing problem andthe origin of large uncertainties in the reconstruction of the mass of the high energy primarycosmic rays. Hadronic interaction models, re-tuned after early LHC data, have a more consistentdescription of the muon content among them but still disagree with data. Collective hadronizationdue to the formation of a quark gluon plasma (QGP) has already been studied as a possible cause fora larger production of muons under extreme conditions (rare, very central nuclear interactions), butwithout real success. However, in the view of the most recent LHC data, a collective hadronizationphase might not only be limited to such extreme conditions. And because of its different ratioof electromagnetic to hadronic energy, a QGP may have the properties to solve the muon puzzle.This hypothesis is demonstrated using a theoretical approach and tested in a proper way by themodification of hadronic model spectra in CONEX to mimic the production of a QGP also in lessextreme conditions with a possible large impact on air shower physics.

37th International Cosmic Ray Conference (ICRC 2021)July 12th – 23rd, 2021Online – Berlin, Germany

∗Presenter

© Copyright owned by the author(s) under the terms of the Creative CommonsAttribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). https://pos.sissa.it/

mailto:[email protected]

https://pos.sissa.it/

PoS(ICRC2021)469

Collective hadronization and muon puzzle Tanguy Pierog

1. Introduction

Despite all the efforts made to take into account the first results of proton-proton collisions at theLHC in hadronic interactionmodels used for air-shower simulations, the observed number ofmuons,their height of production or even the depth of shower maximum are still not reproduced consistentlyby themodels [1]. Furthermore, the differences inmodel predictions introduce uncertainty in cosmicray data analysis which are less than in the past but still exceed the experimental uncertainty incertain cases [2]. But before claiming for the need for “new physics”, it is important to guaranteethat all the QCD standard physics is properly taken into account in these models. For that it isnecessary to go beyond the simplest observables which are usually used to test them. The variousLHC experiments provided a large amount of complex data to analyze and understand, in particularthanks to the correlation between different observables, which are not yet fully investigated.

Among the hadronic interaction models used for air-shower analysis, only Epos lhc [3–6]includes all the features needed to have a detailed description of the correlation between variousobservables [1]. Indeed the core-corona approach in this model, which allows the production of acollective hadronization phase, appears to be a key element to reproduce LHC data. Before LHC, itwas usually accepted that hydrodynamical phase expansion due to the formation of a quark-gluonplasma (QGP), for instance, was possible only in central heavy-ion collisions. Proton-nucleus (pA)collisions were then used as a reference to probe the effect of such collective behavior (final state)but with some nuclear effect at the initial state level, while proton-proton (pp) interactions werefree of any nuclear effects. With the LHC operated in pp, pPb and PbPb mode, it is now possible tocompare high-multiplicity pp or pPb events with low-multiplicity PbPb events (which correspond tothe same number of particles measured at mid-rapidity) and surprisingly the very same phenomenaare observed [7, 8] concerning the soft-particle production.

One of the most striking features observed in all systems is the long-range two-particle corre-lations and the evolution of the particle flow as described in [9]. In [10] the authors demonstratehow these data from the CMS Collaboration can be reproduced and explained using an approachcombining standard perturbative calculations for initial conditions and hydrodynamical calculationsfor the final state interactions.

At the same time, the recent results compiled by theWHISPworking group [11] clearly indicatethat the discrepancy in the muon production between simulations and data, gradually increase withenergy. It is a strong indication of a different hadronization than the one used in the current hadronicmodels [12–16], including Epos lhc, which doesn’t have enough core contribution according todata [7] published after the release of the model in 2012.

In [17], we present a modified version of Epos lhc [4] based on Epos3 [3] to study theconsequence of the extended range of collective hadronization on air-shower physics in this particularmodel with positive results on the number of muons. To have a more general approach, new resultsbased on modified secondary particle spectra following the core-corona approach applicable to anymodel are now presented.

In Section 2, we will discuss the impact of collective hadronization in the total number ofmuons produced by air showers. In Section 3 the basic principles the core-corona approach willbe presented and we will discuss the changes made in CONEX [18] to take this modifications intoaccount. Finally, in Section 4, we will discuss future developments.

2

PoS(ICRC2021)469


2. Collective hadronization and Air-shower physics

The dominant mechanism for the production of muons in air showers is via the decay of lightcharged mesons. The vast majority of mesons are produced at the end of the hadron cascadeafter typically five to ten generations of hadronic interactions (depending on the energy and zenithangle of the cosmic ray). The energy carried by neutral pions, however, is directly fed to theelectromagnetic shower component and is not available for further production of more mesons andsubsequently muons. Thus, the energy carried by hadrons that are not neutral pions is typically ableto produce more hadrons and ultimately muons in following interactions and decays. As explainedin [12, 19], the ratio of the average electromagnetic to average hadronic energy, called ', and itsdependence on center-of-mass energy, is thus related to the muon abundance in air showers: ifthis energy ratio is smaller (larger), more (less) energy is available for the production of muonsat the end of the hadronic cascade and ultimately more (less) muons are produced. In fact it caneven be demonstrated in the simple Matthews-Heitler model [20] that the exponent V of the energydependence of the muon production is directly related to ' as V = 1 + ln(1 − 2)/ln(#all) where#all is the total multiplicity and 2 = #c0/#all and thus ' = 2/(1 − 2) if all particles have the sameenergy like in this simplified model.

Since in a collective hadronization (or statistical model) the production of particles with highermass (in particular with strange quarks) [21] is not suppressed as in a string hadronization, thefraction of secondary pions in the dense core is reduced because many other more massive hadronsand resonances are produced. This leads to a lower ratio of the electromagnetic to hadronic energydensity in particles produced from the core. As a consequence, such reduction of ' due to morecollectivity in secondary particle production should increase the slope V of the energy dependenceof the muon production in air showers compare to traditional hadronic models where only the stringhadronization is taken into account.

3. Core-corona effect

The discussion in the previous section suggests that a change of ' is a potential way to reducethe discrepancy between measurements and air shower simulations. Nevertheless, ' is quite wellconstrained by theory as well as laboratory measurements and, thus, can not be changed entirelyarbitrarily as studied in an other analysis [22]. In a naive model like Ref. [20] where only pionsare considered as secondary particles, ' = 0.5. In a more realistic approach based on stringfragmentation we have ' ≈ 0.41 − 0.45.

But as shown in Ref. [7], particle ratios such as /c, ?/c or Λ/c change with increasingsecondary particle density, saturating to the value given by a thermal/statistical model with afreezeout temperature of 156.5MeV [23] yielding ' ≈ 0.34. Such a behavior can be explainedin terms of a core-corona picture [21]. This approach has been used in the framework of realisticsimulations [24], but also in simple model calculations [25–28]. The basic idea is that some fractionof the volume of an event (or even a fraction of events) behaves as a quark gluon plasma and decaysaccording to statistical hadronization (core), whereas the other part produces particles via stringfragmentation (corona). The particle yield #8 for particle species 8 is then a sum of two contributions

#8 = lcore #core8 + (1 − lcore) #corona

8 , (1)

3

PoS(ICRC2021)469


10-4

10-3

1 10 102

103

<dnch

/dη(0)>

rati

o t

o π ALICE (black)

ΩEPOS 3.210

fullco+cocoronacore

102 103 104 105 106 107 108 109 1010

Elab/GeV

0.0

0.1

0.2

0.3

0.4

0.5

0.6

R=

Eem/E

had

Mid-Rapidity

p + airinteraction

EPOS-LHCQGSJET-II-04SIBYLL-2.3dCorona only ( fω = 0)

fω = 1.00 ,Escale = 1010 GeV

Core only

Figure 1: Left-hand side: Particle to pion ratio for theΩ baryon versus multiplicity at mid-rapidity, for differ-ent contributions (core (dash-dotted), corona (dotted), core+corona (dashed) and all (core+corona+hadronicgas) (full)) from the epos simulations, for different systems (pp (thin), pPb (normal), PbPb (bold)). We alsoplot ALICE data from [7]. Right-hand side: evolution of the ratio R from pure corona to pure core in case oflinear increase of core fraction as a function of the logarithm of the energy for 3 different models in proton-airinteractions at mid-rapidity.

where #core8

represents statistical (grand canonical) particle production, and #corona8

is the yieldfrom string decay. Crucial is the core weight lcore. In order to explain LHC data [7] the weightlcore needs to increase monotonically with the multiplicity, starting from zero for low multiplicity? − ? scattering, up to 0.5 or more for very high multiplicity ? − ?, reaching unity for central heavyion collisions (PbPb) as illustrated in Fig. 1 using Epos3 model [3].

In order to know whether such a constrained value of ' could be low enough to increase thenumber of muons in air shower simulations such that the data could be reproduced, a simplifiedcore-corona approach can be used to at least set some realistic upper-limit under the followingassumptions :

• the fraction of core effectively increase with energy: the core-corona approach is originally asa function of the multiplicity and independent of the collision energy for a given multiplicity.Since the averagemultiplicity increasewith the energy, the average core fractionmust increasewith energy.

• only the change in hadronization is taken into account: collective effects in core in principleincludes particle correlations and flow, but since the longitudinal particle momentum isdominating over the transverse momentum down to relatively low energy, these effects canbe neglected in first order.

• no nuclear effect is introduced: the multiplicity increase with the mass of the projectile, sothe core fraction would increase for higher primary mass. This is not taken into account dueto technical limitations (minimizing the effect for higher primary mass but only for the firstfew hadronic generations).

4

PoS(ICRC2021)469


• core-corona effect is applied on full phase space: core hadronization has been observed atmid-rapidity, but in order to see the maximal effect on air shower to set an upper-limit, themodification should apply at larger rapidities.

So in the following, we are going to employ a straightforward core-corona approach, based oneq. (1), for any hadronic interaction model in CONEX air shower simulations. The particle yieldfrom the chosen interaction model is by definition considered to be the corona yield, whereas weuse the standard statistical hadronization (also referred to as resonance gas) for the core part. Solcore = 0 would be the “normal" simulation with the default interaction model. Choosing lcore > 0amounts to mixing the yields from the interaction model according to the core-corona superpositionshown in eq. (1) and depicted in Fig.. 1 right-hand side for proton-air interactions for 3 differenthadronic interaction models Epos lhc, QGSJetII.04 [29, 30] and Sibyll 2.3d [31].

Technically, we directly modify individual particle ratios of the secondary particle spectrad#8/d 9 , for particle species 8 and energy bins d 9 , of hadronic interactions with air nuclei usedby CONEX for numerical air shower simulations based on cascade equations. Knowing the initialratios c0/c±, ?/c±, ±/c±, ?/=, 0/ ± (taking into account strange baryon decays) from a coronatype model and the value of the same ratios from the core model, we compute new spectra inwhich the particle yields include both, core and corona according to lcore. Since the hadronizationmechanism can affect only newly produced particles the properties of the leading particle should bepreserved. To achieve that, the new particle yields are computed for all secondaries, but excludingthe one corresponding to the respective projectile type, i.e. protons in proton-air, kaons in kaon-airinteractions, and so on. The yield of the projectile-type particles is determined subsequently byexploiting energy conservation in all energy bins d 9 summed over all secondary particle species8: the sum

∑8 9d#8/d 9 must be conserved. Since at high GF = j/lab only the projectile-

type particles will have d#8/d 9 significantly different from zero (aka leading-particle effect), theresulting modified leading-particle type spectra at high GF follow the original distribution, and areonly affected by the scaling procedure at lower values of GF. Together, this assures that energyconservation as well as the total multiplicity are not affected, but only the particle ratios. Moredetails will be given in a future publication.

We expect the core weight lcore to increase with energy in a logarithmic way like the totalmultiplicity. Thus, we use

lcore(lab) = 5l (lab; th, scale) (2)

with (lab; th, scale) =

log10(lab/th)log10(scale/th)

for lab > th, (3)

to model this, starting already at fixed-target energies, th = 100GeV. Different energy depen-dencies are explored by changing scale from 100GeV (corresponding to a step function), to106 GeV, and 1010 GeV. The 5l scale is varied from 0.25, 0.5, 0.75 to 1.0; in addition we enforce (lab; th, scale)

!= 1 for all lab ≥ scale. This yields thelcore energy dependencies as depicted in

Fig. 2 left-hand side. All these scenarios have been used to simulate full air showers with CONEX,using cascade equations from the first interaction to the ground, for proton and iron primary particlesat 0 = 1019 eV. In Fig. 2 the results are shown in the -max-ln#` plane for QGSJetII.04. Thistypical example illustrate that it is well possible with modified hadronization in air shower cascades

5

PoS(ICRC2021)469


102 103 104 105 106 107 108 109 1010

Elab / GeV

0.00

0.25

0.50

0.75

1.00

1.25

ωco

re

fω = 1.00 ,Escale = 102 GeV


fω = 1.00 ,Escale = 1010 GeV

fω = 0.75 ,Escale = 1010 GeV

fω = 0.50 ,Escale = 1010 GeV

fω = 0.25 ,Escale = 1010 GeV

700 720 740 760 780 800〈Xmax〉/gcm−2

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

〈lnN

µ〉−

lnN

ref

µ

p

Fe

Auger 2015

E0 = 1019 eV



fω = 1.00 ,Escale = 1010 GeV

fω = 0.75 ,Escale = 1010 GeV

fω = 0.50 ,Escale = 1010 GeV

fω = 0.25 ,Escale = 1010 GeVfω = 0 (Default model)

QGSJetII.04

Figure 2: Left-hand side: Different energy evolutions probed for lcore. The solid lines represent changingthe scale 5l of the effect, while the dashed lines also indicate the effect of changing scale. Right-hand side:Comparison of different core-corona mixing scenarios, as described in the text, on air shower simulationsat 1019 eV QGSJetII.04 in the -max-ln#` plane. The solid lines represent changing the scale 5l , while thedashed lines also indicate the effect of changing scale. The default model corresponds to the corona-onlysimulations. The datum is from the Pierre Auger Observatory [32]. Each model line represents all valuesthat can be obtained for any mixture of cosmic nuclei from proton (bottom right) to iron (top left).

to describe the data of the Pierre Auger Observatory. As expected, more core-like contributions areneeded compared to what is currently provided by the models. This means, QGP-like effects alsoin light colliding systems and starting in central collisions at much lower center-of-mass energiesmay play a decisive role.

4. Summary

The better description of the collective hadronization and in particular the fact that the core isproduced earlier than predicted by Epos lhccan have very important consequences for the muonproduction in air showers. The effect of QGP using the standard Epos lhcwas shown not to besignificant. Indeed in this model, the QGP was produced only for very high-multiplicity eventsand at mid-rapidity which are both rare and not so important for air-shower development. Otherstudies using a QGP or alternative hadronization as a possible new source of muons were all basedon changes under extreme conditions too [13, 34] or with extreme consequences not observed atthe LHC [14]. As shown here and in [33], according to the most recent LHC results, the collectivehadronization happens at a much lower multiplicity and as a consequence with effects at largerrapidities (lower particle densities than foreseen). In that case, much more particles coming fromthe hadronization of a QGP play a significant role in the air-shower development. The productionof the QGP is increasing with energy (since the multiplicity increases) leading to a reduce ratio 'between energy going into electromagnetic particles and energy carried by hadronic particles andas a consequence the slope of the energy dependence of the muon production also increase with theprimary energy and is closer to the one observed by the WHISP working group [11] in the data,and without changing the 〈-max〉 too much. A stronger effect could be observed in case of nuclearprojectile with could create a collective phase with a non zero chemical potential which could leadto an even stronger increase of the non electromagnetic secondary particles [16]. The combinationof a mild increase like observed in this study with a proton primary with an even stronger effect for

6

PoS(ICRC2021)469


heavier projectile could be the complete solution of the muon deficit in air shower simulations. Amonte-carlo model taking into account the core-corona effect in a detailed enough way to reproduceall major effects observed at the LHC is still under development [35]. More data in particular inforward phase space from LHCb [36, 37] or other projects [38] and using light ion beam lightoxigen at the LHC is required to set further constraints on the core-corona mechanism.

References

[1] T. Pierog, PoS ICRC2017, 1100 (2018)

[2] K.H. Kampert, M. Unger, Astropart.Phys. 35, 660 (2012), 1201.0018

[3] K. Werner, B. Guiot, I. Karpenko, T. Pierog (2013), 1312.1233

[4] T. Pierog, I. Karpenko, J.M. Katzy, E. Yatsenko, K. Werner, Phys. Rev. C92, 034906 (2015),1306.0121

[5] K.Werner, I. Karpenko, T. Pierog, M. Bleicher, K. Mikhailov, Phys. Rev.C82, 044904 (2010),1004.0805

[6] K. Werner, F.M. Liu, T. Pierog, Phys. Rev. C74, 044902 (2006), hep-ph/0506232

[7] J. Adam et al. [ALICE], Nature Phys. 13, 535-539 (2017) 1606.07424

[8] J. Pan (ALICE), J. Phys. Conf. Ser. 832, 012044 (2017)

[9] V. Khachatryan et al. (CMS), Phys. Lett. B742, 200 (2015), 1409.3392

[10] K. Werner, J. Phys. Conf. Ser. 636, 012006 (2015)

[11] H. Dembinski, et al. (EAS-MSU, KASCADE-Grande, IceCube, NEVOD-DECOR, PierreAuger, SUGAR, Telescope Array, Yakutsk EAS), EPJ Web Conf. 210, 02004 (2019)1902.08124

[12] S. Baur, H. Dembinski, T. Pierog, R. Ulrich, K. Werner, To be published in Phys. Rev. D(2019) 1902.09265

[13] J.F. Soriano, L.A. Anchordoqui, T.C. Paul, T.J. Weiler, PoS ICRC2017, 342 (2018),1811.07728

[14] J. Alvarez-Muniz, L. Cazon, R. Conceição, J.D. de Deus, C. Pajares, M. Pimenta (2012),1209.6474

[15] G.R. Farrar, J.D. Allen, EPJ Web Conf. 53 07007 (2013) 1307.2322

[16] L.A. Anchordoqui, H. Goldberg, T.K. Weiler, Phys. Rev. D95, 063005 (2017) 1612.07328

[17] T. Pierog, S. Baur, H. P. Dembinski, R. Ulrich and K. Werner, PoS ICRC2019, 387 (2020)

7

PoS(ICRC2021)469


[18] T. Bergmann, R. Engel, D. Heck, N. N. Kalmykov, S. Ostapchenko, T. Pierog, T. Thouw andK. Werner, Astropart. Phys. 26, 420-432 (2007) astro-ph/0606564

[19] T. Pierog, K. Werner,Phys. Rev. Lett., 171101 (2008), astro-ph/0611311

[20] J. Matthews, Astropart. Phys. 22, 387 (2005)

[21] K. Werner, et al., EPJ Web Conf. 17, 10900 (2018) 1812.06330

[22] R. Ulrich, R. Engel and M. Unger, Phys. Rev. D 83, 054026 (2011) 1010.4310

[23] A. Andronic, P. Braun-Munzinger, K. Redlich and J. Stachel, J. Phys. Conf. Ser. 779 no.1,012012 (2017) 1611.01347

[24] K. Werner, Phys. Rev. Lett. 98, 152301 (2007) 0704.1270

[25] J. Manninen and F. Becattini, Phys. Rev. C 78, 054901 (2008) 0806.4100

[26] F. Becattini and J. Manninen, J. Phys. G 35, 104013 (2008) 0805.0098

[27] J. Aichelin and K. Werner, Phys. Rev. C 82, 034906 (2010) 1001.1545

[28] J. Aichelin and K. Werner, Phys. Rev. C 79, 064907 (2009) [erratum: Phys. Rev. C 81, 029902(2010)] 0810.4465

[29] S. Ostapchenko, Phys. Lett. B 636, 40-45 (2006) hep-ph/0602139

[30] S. Ostapchenko, Phys. Rev. D 81, 114028 (2010) 1003.0196

[31] F. Riehn, R. Engel, A. Fedynitch, T. K. Gaisser and T. Stanev, Phys. Rev. D 102, no.6, 063002(2020) 1912.03300

[32] A. Aab et al. [Pierre Auger], Phys. Rev. D 91, no.3, 032003 (2015) [erratum: Phys. Rev. D91, no.5, 059901 (2015)] 1408.1421

[33] L. A. Anchordoqui, C. García Canal, S. J. Sciutto and J. F. Soriano, Phys. Lett. B 810, 135837(2020) 1907.09816

[34] D. LaHurd, C.E. Covault, JCAP 1811, 007 (2018), 1707.01563

[35] T. Pierog, B. Guiot, I. Karpenko, G. Sophys, M. Stefaniak and K. Werner, EPJWeb Conf. 210,02008 (2019)

[36] A. A. Alves, Jr. et al. [LHCb], JINST 3, S08005 (2008)

[37] R. Aaĳ et al. [LHCb], Int. J. Mod. Phys. A 30, no.07, 1530022 (2015) 1412.6352

[38] M. G. Albrow, 2006.11680

8

Documents

When heavy ions meet cosmic rays: potential impact of QGP